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Fast diffusion inhibits disease outbreaks. (English) Zbl 1441.92041

In this paper, using recent advances in the spectral theory of linear operators, the authors show that the basic reproduction number of a multipatch SIS model is strictly decreasing and strictly convex in the diffusion coefficient for the infected subpopulations, thus completely solving and generalizing a conjecture by L. J. S. Allen et al. [SIAM J. Appl. Math. 67, No. 5, 1283–1309 (2007; Zbl 1121.92054)]. The biological meaning of the result is that fast diffusion of infected individuals reduces the risk of infection. The authors also obtain an improved lower bound on the multipatch reproduction number, a generalized monotone result on the spectral bound of the Jacobian of the model at the disease-free equilibrium, and the limit of the endemic equilibrium as the diffusion coefficient tends to infinity. An important note is that the influence of diffusion on disease persistence is strongly affected by the model structure and strict monotonicity of the basic reproduction number with respect to the diffusion coefficient of infected may fail for differently formulated models, hence further investigations are required in this matter.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations

Citations:

Zbl 1121.92054
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Full Text: DOI arXiv

References:

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